Abstract

There is a huge literature devoted to the topic of estimator selection, both from a theoretical and a practical view point. Estimator selection methods typically involve tuning parameters which drastically influence the behaviour of the methods. Therefore the choice of these tuning parameters is an important issue. It is often the case that performance bounds for estimator selection methods are over pessimistic or not precise enough to provide a valuable guide-line for practitioners. Fortunately computer intensive simulations can be used to understand how to calibrate these tuning parameters in practice but nevertheless from a mathematical view point, it is desirable to better understand the issue of calibrating selection methods. We shall see that in a number of situations that include penalized model selection, it is possible to reduce the gap between theory and practice by providing data-driven rules for choosing tuning parameters which are based on sharp upper and lower performance bounds.